Process and apparatus for determination of spinodal and critical points or loci associated with phase transition

ABSTRACT

In a method of determining spinodals, and particularly critical points, associated with phase transitions in samples of chemical solutions, a sample is subjected to relatively fast thermal pulses, and measurements of a physical variable of the solution are concurrently made. The physical variable may be any property, such as light-scattering intensity, the value of which property varies strongly around the spinodal or critical point. The thermal pulses may, for example, be applied to the sample by means of two fluid baths controlled at different temperatures, the temperature of one bath being changed slowly. Fluid is passed from the two baths, alternately, into heat-exchange relationship with the sample. In an alternative apparatus, a single fluid bath may be used, the fluid being passed into heat-exchange relationship with the sample either without further heating or with further heating by a heater adjacent to the sample.

United States Patent [1 1 Gordon et al.

[ Apr. 30, 1974 PROCESS AND APPARATUS FOR [54] 3,187,557 6/1965 Holboume 73 17 R DETERMINATION OF SPINODAL AND 3,457,772 7/1969 Chassagne et a]. 73/17 R CRITICAL POINTS 0R LOCI ASSOCIATED 3,545,254 l2/l970 Classagne et al. 73/17 R WITH PHASE TRANSITION Primary ExaminerRonald L. Wibert [76] Inventors: Manfred Gordon, The Moorings, 11 As i tan Examiner-F, L, Evans Belle V116 Wiveflhoe, g Attorney, Agent, or Firm-Hubbell, Cohen & Stiefel John McKenzie Grant Cowie, 53 Chalton Rg; Bridgevolti Allan, 57 ABSTRACT I I 53 6:2 3: ga 3 gg gffi In a method of determining spinodals, and particularly 10 chestgut both of g critical points, associated with phase transitions in sam les of chemical solutions, a sample is subjected to Colchester England p relatively fast thermal pulses, and measurements of a [22] Filed: Dec. 16, 1971 physical variable of the solution are concurrently made. The physical variable may be any property, [21] Appl' 208782 such as light-scattering intensity, the value of which property varies strongly around the spinodal or critical [30] Foreign Application Priority Data point. The thermal pulses may, for example, be ap- Dec. 18, 1970 Great Britain 60,171/70 plied to the Sample y means of two fluid baths i trolled at different temperatures, the temperature of 52 US. Cl. 356/103, 73/17 R one bath being changed y- Fluid is passed from 51 Int. Cl. G01n 25/12, 00111 21/24 the two baths, alternately, inte heat-exchange relation- [58] Field of Search 356/103, 104; 73/17 R p With the sample In an alternative apparatus, a

- single fluid bath may be used, the fluid being passed 56 References Cited into heat-exchange relationship with the sample either UNITED STATES PATENTS without further heating or with further heating by a heater adjacent to the sample.

3,008,324 11/1961 Rayford et al. 73/17 R 3,031,880 5/1962 Findlay 73/17 R 12 Claims, 9 Drawing Figures a T 11 h ,wg Till 4H 5 3 l,

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PROCESS AND APPARATUS FOR DETERMINATION OF SPINODAL AND CRITICAL POINTS OR LOCI ASSOCIATED WITH PHASE TRANSITION Among the methods employed for the characterization of chemical compounds is that of measurement of their cloud points when dissolved in solvents at varying degrees of concentration. Such measurements are made by slowly reducing or increasing the temperature of their solutions, according to whether or not the solubility coefficient is positive or negative, until the onset of turbidity is reached. This point lies at or near the temperature at which the solution passes from the stable to the metastable state. The proximity of the observed cloud point to the actual temperature at which this transition occurs, hereinafter referred to as T at any particular concentration is influenced by the rate of temperature change. For a given system the set of cloud points form a continuous locus, for example the cloud point versus concentration curve in the case of a system of binary solutions.

The values of cloud point and T are theoretically coincident only when the rate of heating (or cooling) is infinitely small. In practice the cloud point is generally regarded as coincident with T provided merely that the measurement has been made under conditions of sufficiently slow temperature change. As the rate of cooling (or heating) is increased the observed cloud point can be expected to fall short of (or exceed) T until a sufficiently fast rate of cooling (or heating) is reached when the cloud point coincides with the point at which the solution passes from the metastable to the unstable state. The border between the metastable and the unstable states is known as'the spinodal temperature and will be denoted by T The set of spinodal temperatures of a system is called the spinodal locus. For instance in a binary system the spinodal locus consists of the spinodal temperature versus concentration curve. If the temperature of a solution is brought by sufficiently fast temperature change to a point on the spinodal locus substantially without prior phase separation it will then undergo the so-called spinodal decomposition which is an extremely rapid separation of phases. In practice this phenomenen has eluded measurement because of heat transfer limitations upon the rate of temperature change in any device suitable for making measurements. For instance R. Koningsveld has stated that spinodals cannot be measured in Advances in Colloid and Interface Science, (Vol. 2, 1968, p. 178).

The critical point of a solution is defined as the point of tangency between the locus of T and the locus of spinodal temperatures T For a binary system the critical locus comprises only isolated critical points but for a ternary system the critical locus is a curve comprising the set of critical points in a plot of temperature versus some measure of composition of the solution. At any critical point the state of the solution is on the border between stable and unstable conditions without any states of metastability intervening between the two.

GIBBS DEFINITION OF THE SPINODAL According to Willard Gibbs (Collection Works, Vol. 1, p. 132, Dover Publications Reprint, 1961), the spinodal is given by for any number of components; and 4:, are the independant composition variables and AG is the free enthalpy of mixing.

SPINODAL DECOMPOSITION The intensity of the light scattered by a solution is determined by inhomogeneities of the refractive index of the solution. So called critical scattering is due to fluctuations in both the density and the concentration. The fluctuation theory and its extension to solutions of polydisperse polymers show that there is a definite relationship between the intensity of the scattered light and the second derivatives of the free enthalpy (Gibbs free energy) of mixing with respect to the concentration of the polymer components..The detailed theory shows that in the vicinity of the spinodal the scattered light intensity will increase the very high values.

For convenience, we shall denote by particle a region in the solution which scatters light irrespective of whether it is (a) an actual phase boundary or (b) produced by concentration fluctuations. Cases (a) and (b) generally lead to particles differing in size distribution as well as in nature and hence in scattering behaviour. On cooling or heating a solution slowly towards a cloud point (which is not close to a critical point), fluctuations and the scattering produced by them are generally weak. As the cloud point is passed, particles with definite phase boundaries grow and the scattering increases. On cooling or heating a solution rapidly, however, very strong critical scattering due to metastable particles generated by fluctuations is observed below T and as the spinodal is approached.

The occurance of spinodal decomposition can, therefore, in principle be detected by measurements which respond to change in the nature and size distribution of particles such as light scattering or turbidity measurements.

In order to measure spinodal points, we have found a method of overcoming the difficulty of reconciling fast rates of temperature change with sufficiently accurate measurements of the state of the solution by scattering.

While it is clearly advantageous to the study of phase separation in solution that a method of observing spinodals is available it is of particular advantage that rapid measurements of spinodals and critical points can now be made in respect of solutions of polymers. This particular significance lies in the close relationship between the spinodal of a system of polymer solutions and the weight average molecular weight m of the polymer and between the critical point of a system of polymer solutions and the z-average molecular weight m of the polymer. The exact relationships have been described in a publication by M. Gordon, R. Koningsveld and H.A.G. Chermin, Macromolecules", Vol. 2, page 207 (1969), for a realistic model theory. According thereto the following expressions can be written for Critical State (8 ill/84 m Z m t, 2 (l )'2 where \IJ g l) 4) is the volume fraction, g is a semiempirical interaction parameter, and m w and m z are the weightand z-average chain lengths.

The object of this invention is to provide a process whereby the aforementioned spinodal and critical loci of systems of solution can be measured to acceptable degrees of accuracy and the apparatus by which such measurements may be performed.

The drawings show prefered embodiments of the invention as well as diagrams related to the invention:

FIG. 1 shows an example of experimental record of light intensity values produced by a series of temperature pulses on a sample of polystrene in cyclohexane.

FIG. 2 shows the extrapolation procedure for the determination of the spinodal temperature.

FIG. 3 shows the block diagram of a two bath flow system.

FIG. 4 shows a block diagram of a single bath flow system.

FIG. 5 shows a longitudinal section of a measurement section.

FIG. 6 shows a cross section of a measurement section (similar to FIG. 5).

FIG. 7 shows an experimental record for determination of the cloud point.

FIG. 8 shows experimental spinodal and cloud point curves for a series of solutions of a sample of polystyrene in cyclohexane.

FIG. 9 shows experimental spinodal curves obtained for two samples of polystyrenes with different molecular weights.

It has been found that the region T to T can be spanned by a series of thermal pulses which can be used to explore the scattering in this region. The preferred procedure for carrying out the thermal pulses is described below. A sample of a transparent solution of a compound in a solvent in which for example its solubility decreases with decreasing temperature, is cooled rapidly from a temperature T just above T to a temperature T just below T the solution being held at that temperature T for some period of time, and then reheated to to a temperature above T for example, T The cooling and reheating cycles continue, each rapid cooling step being taken to a temperature 'I' incrementally lower than that of the previous step, until the region from T to T has been spanned. The scattering-or turbidity of the solution caused by each temperature pulse is measured, for example by light scattering. An example of such measurement is shown in FIG. 1. A spinodal temperature results from the analysis of turbidity or intensity of scattered light as a function of the temperatures T of the consecutive steps. For example, the valve of T may be taken as the temperature at the inflexion of the curve of intensity J versus T However, a more accurate determination of the spinodal temperature results from the extrapolation of the plot of reciprocal intensity l/J versus temperatu re to zero, i.e., to infinite intensity as shown in FIG.

2. It will be realized that it is the linear portion of the curve of ill versus temperature which has to be extrapolated, as shown in FIG. 2. A series of such spinodal temperatures obtained from solutions of the compound in the same solvent at different concentrations enables the spinodal locus of the solution to be obtained.

A comparable plot of cloud point temperatures T versus concentration may be conveniently made using the same apparatus with the same samples, either by cooling to a temperature at which the turbidity occurs, sufficiently slowly to ensure that the onset of turbidity occurs at a temperature of reasonable proximity to T,,,, or more quickly by heating a phase separated solution at the constant rate resulting in a fall in the scattered intensity, when T is found as a kink in the plot of J versus T at which the scattering changes from the regime of particle scattering to that of scattering by concentration fluctuations. The resultant plot of the cloud points versus concentration can then be used to determine the critical solution temperature of the sample in the particular solvent. The critical solution temperature is the point of tangency between the plots of T and T against concentration. Thus both the spinodal curve and the cloud point curve are measured in order to determine the critical solution temperature.

With regard to FIG. 3 an apparatus according to the invention comprises at least one transparent capillary cell 1, of such dimensions that it has a negligible or substantially negligible heat capacity in comparison with its environment, which contains the sample of the solution to be examined, inserted into a fluid flow system 2 through which a light beam 3 from a light source 4 is transmitted and through which scattered light, generated by turbidity, is transmitted in such a manner that its intensity can be measured and means 5 for sensing at any desired angle and means 6 for measuring and optionally recording the aforesaid scattered light. The aforesaid fluid flow system 2 is equipped for means of rapid temperature changes. One preferred means is to connect the flow system to at least two fluid containing baths, 7, 8 of which, in the case of measuring spinodals, one (7) is maintained at the temperature T,, preferably with thermostatic control 9 and the other (8) at temperature T capable of being changed to other temperatures T by means of thermostatic control 10. The aforesaid flow system 2 embodies a pump 11 and valve arrangement l2, 13 which permits switching the flow of fluid around the capillary cell 1 alternatively from the source at T, to the source at T A repeated switching of the valve arrangement l2, 13 causes temperature pulses in the capillary cell ll between fixed temperature T and slowly changing temperature T It is also preferred that a means 14 for accurately measuring the temperature in the vicinity of the capillary cell, at times coincident or substantially coincident with those at which turbidity measurements are made, is incorporated into the fluid flow system. If desired the aforesaid temperatures may be simultaneously recorded by means 6.

An alternative means of carrying out spinodal decomposition is the use of a single bath flow system. Such a system is shown schematically in FIG. 4. This apparatus consists of a bath 17 containing a heat transfer fluid -l8, heated by means of an electric immersion heater 19, or cooled by a refrigeration unit 20. The

' heat transfer fluid 18 is capable of being pumped by pump 21 around the cell 1, cell heater 26 and back into the bath 17. A light source 4 and measuring means 5 are provided for light scattering measurements and temperature sensing means 14 located in the heat transferfluid in the vicinity of the capillary cell 1 is employed to measure the temperature while the light scattering measurements are made. The thermometer l4 and the light sensor 5 are connected to a data handling system 23.

The measurement section of the apparatus is shown in more detail in FIG. 5 and FIG. 6. In these diagrams the light source is denoted by 4. The capillary cell 1 containing the samples is sealed with silicone rubber in a cell holder 24, which is positioned in the wall of a flow tube 25. The immersed cell heater 26 is connected to a power supply (not shown) by means of connecting rods 27. In this example of the apparatus, the heater 26 has a capacity of 60 Watts. The heater 26 is situated a convenient distance from the cell I; typically this .is 1mm. The thermometer l4 and the light sensor 5 are located approximately at the positions shown, however the light sensor 5 may be located in different positions when the angular dependance of the scattering is measured. The direction of the flow of the heat transfer fluid is indicated by arrow 28. The aforesaid transparent capillary cell 1 is essentially fabricated from a material resistant to attack or dissolution by either the solution being examined or the surrounding heat transfer fluid 18. For the examination of most solutions it can conveniently be fabricated from glass. Its dimensions should be such that its external volume is of a low order in comparison with the volume occupied by the surrounding region of the fluid flow system 2. It is preferred that its size shall be conveniently small in order both to facilitate rapid heat transfer and to enable small quantities of solution to be examined. It has been found that a convenient capillary cell 1 may be fabricated from glass tubing of approximately 1.4mm. external diameter and 1.0mm bore. Having sealed one end of the aforesaid glass tubing a sample S of the solution to be examined is introduced therein to occupy a length of approximately 1 /2 to 2 A cm. the tubing is then drawn off and sealed as close to the upper meniscus of the s mple as convenient. It should be understood that the oresaid dimensions should not be limiting. The cell holder 24 is so designed that light from an incident beam, as described, can be transmitted along the longitudinal axis of the capillary cell 1.

The incident light beam may be derived either from a laser source or collimated ordinary light, if desired however radiations of selected wavelength, such as ultra-violet or X-rays, may also be employed. In general, however the light source may be selected according to the precise solute-solvent system being examined. Scattered light is transmitted through the cell wall and is received either directly by a sensor 5 or via a light guide (not shown) or alternatively the scattered radiation may pass through windows suitably positioned in the wall of the fluid flow system.

While it is not desired to limit the internal dimensions of the fluid flow system 2 in the vicinity of the capillary cell 1 and light scattering region, other than to state that cross-sectional size and shape should be such as to comfortably house the aforesaid capillary cell 1, it has been found convenient to accomodate a capillary cell 1 of dimensions hereinbefore described in a fluid flow system 2 of circular cross-section and approximately 3 cms internal diameter in the plane containing the cell 1 and incident light beam.

MODE OF OPERATION The apparatus according to FIG. 4 can for example be used in the following way to determine spinodals in the vicinity of an upper critical solution temperature: The temperature of the fluid 18 is adjusted to a value above the cloud point for the particular solution being studied. The cell heater 26 is then switched on, causing the temperature in the vicinity of the capillary cell 1 to rise to T The temperature of the fluid 18 is then adjusted to a lower temperature level T which is nearer the cloud point temperature, and then the cell heater 26 is switchedoff. The action of switching off the cell heater causes the temperature of the sample in the cell to fall rapidly from T to T The scattered light produced and the temperature are recorded. The cell heater 25 is then switched on again; this causes the temperature of the sample to rise to T The next step in the process is that the temperature T of the fluid bath is lowered to a new T incrementally below the foregoing T The cell heater is then switched off and the measurements repeated. This procedure is then carried out fora series of T values.

The preferred means of producing T is a slow continuous method, instead of controllng the temperature at discrete values. This has the effect of speeding up the measurements, however, it must be noted that the rate of temperature change must be sufficiently slow so that the temperature is nearly constant over the duration of a pulse e.g. 5 seconds.

An example of the measurements made by the technique described above is shown in FIG. 1. The temperature trace shows a slow rate of cooling in this experiment i.e. 1C 10 minutes. The intensity trace of scattered light shows how the light scattered by the sample S increases to higher values as the spinodal is approached.

FIG. 2 shows as an example the determination of the spinodal temperature by extrapolating to infinite intensity values of the scattered light. The reciprocal value of the intensity trace, i.e. the peak values of pulses shown in FIG. 1 is plotted against the temperature. A straight line connecting these values intersects the temperature axis at the spinodal temperature.

The apparatus according to FIG. 4 can also be used in the determination of the cloud point temperature. An example of such a measurement is shown in FIG. 7. The cell heater 26 is switched on, to' maintain the sample at T,, meanwhile the temperature of the circulating fluid is adjusted to a value which lies below the cloud point curve, and maintained at that temperature. The cell heater 26 is then switched off, the intensity of scattered light rises to a peak value and then falls to an almost constant value D. At this point the temperature of the circulating fluid 18 is allowed to increase at a constant rate as shown by the curve B. As a result the light intensity decreases. The cloud point temperature C is then determined by the extrapolation procedure shown on this FIG. 7.

The pronounced peak value (FIG. 7) through which the light intensity passes before levelling off at D is an entirely newly-observed phenomenon observed only immediately following a suitable fast temperature step. This observation provides evidence that the solution can be brought into a (metastable) state of large concentration fluctuations in order to make measurements of a physical variable (in the present embodiments, the scattering intensity) which is sensitive to such fluctuations. FIG. 2 shows how the spinodal point is determined by extrapolation based on such maxima. Conventional cloud point measurements have employed heat exchange rates which are too slow to allow observation of the maximum shown in FIG. 7. These conventional measurements operate on scattering intensity levels such as D.

EXAMPLES OF SPINODAL DETERMINATION The single flow apparatus according to FIG. 4 has been used to determine the spinodal locus and the cloud point locus of a sample of Polystyrene (M, 154,000, M 166,000, M 181,000) in cyclohexane. FIG. 8 shows the results of experiments carried out on a series of Polystyrene cyclohexane solutions with concentrations in the range 0.004 to 0.150 weight fraction. The cloud point locus B and the spinodal locus C have a common tangent A which corresponds to the critical solution temperature. The critical concentration, 0.100 weight fraction, and the critical temperature, 296.0 K, are in good agreement with results found by the volume ratio method i.e. critical concentration, 0.102 weight fraction, and a critical temperature of 296.1 K, on the same sample of Polystyrene.

The spinodal curves shown in FIG. 9 were obtained with the two bath flow apparatus. The curve A is the spinodal locus for a Polystyrene sample (M, 154,000, M 166,000, M 181,000) in cyclohexane, the concentration range being 0.01 to 0.15 weight fraction. The curve B is the spinodal locus for a Polystyrene sample (M, 490,000, M 527,000, M, 593,000) incyclohexane, the concentration range being 0.01 to 0.15 weight fraction.

What we claim is:-

1. A process for determining spinodal loci associated with phase transition in samples of chemical solutions, which process comprises l. applying to said sample a series of thermal pulses,

each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample substantially to said first level at which the sample is again stable as a single phase, each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability,

2. measuring the temperature at each said second level for each such applied thermal pulse,

3. measuring, concurrently with the application of the thermal pulses, a physical variable of the sample which changes strongly with temperature around the spinodal point and;

4. determining the spinodal temperature from the measured values of the physical variable and the corresponding measured temperatures.

2. A process as claimed in claim 1, in which the physical variable measured is a change in the distribution of sizes of particles or inhomogeneities.

3. A process as claimed in claim 1, in which the physical variable measured is the intensity of scattered electromagnetic radiation.

4. A process for determining critical loci, said process comprising carrying out the process as claimed in claim 1 and performing cloud point measurements on the sample, the critical loci being determined by using the known thermodynamic condition of tangency relating to critical and spinodal loci.

5. A process for determining spinodal loci associated with phase transition in samples of chemical solutions, which process comprises l. applying to said sample a series of thermal pulses,

each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample substantially to said first level at which the sample is again stable as a single phase,

each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability,

2. measuring the temperature at each said second level for each applied thermal pulse 3. measuring concurrently with the application of the thermal pulses, the intensity of radiation scattered by the sample or the turbidity of the sample, one or more such measurements being effected while the sample is in a metastable state, and

4. locating the spinodal temperature by extrapolation of reciprocal turbidity or reciprocal scattering intensity measurements obtained at the measured temperature levels of the series of pulses.

6. A process for determining critical loci, said process comprising carrying out the process as claimed in claim 5 and performing cloud point measurements on the sample, the critical loci being determined by using the known thermodynamic condition of tangency relating to critical and spinodal loci.

7. Apparatus for determining spinodal loci associated with phase transition in samples of chemical solutions, comprising 1. sample containing means,

2. means for applying to a sample contained in said sample containing means a series of thermal pulses each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample to said first level at which the sample is again stable as a single phase, each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability, said means including a. afirst temperature controlled fluid bath,

b. a second fluid bath having a controlled temperature which is different from that of said first bath,

0. means for slowly changing the temperature of one of said fluid baths, and

(1. means for passing fluid from the baths alternately into heat exchange relationship with the sample containing means to thereby apply said thermal pulses to the sample, said second fluid bath being maintained at a substantially constant temperature at least during each measurement conducted in the hereinafter described measuring means, and

3. measuring means communicating with the sample containing means for measuring a physical variable of the sample, which variable changes strongly with temperature around the spinodal or critical point, whereby-measurements of said variable are made concurrently with the application of the thermal pulses, and at least one said measurement is made while the sample is in a metastable state.

8. Apparatus as claimed in claim 7, comprising means for irradiating the sample with electro-magnetic radiation; means for measuring the intensity of radiation scattered by the sample; and means for measuring the sample temperature.

9. Apparatus as claimed in claim 8 in which said sample containing means comprises a capillary cell.

10. Apparatus for determining spinodal loci associated with phase transition in samples of chemical solutions, comprising l. sample containing means,

2. means for applying to a sample contained in said cent the sample produces the higher temperature cample containing means a series of thermal pulses level of each pulse, and each of which changes the temperature of the sam- 3. measuring means communicating with the sample ple relatively rapidly from a first level at which the containing means for measuring a physical variable sample is in a stable state as a single phase to a secof the sample which variable changes strongly with 0nd level, and subsequently returns the temperatemperature around the spinodal of critical point, ture of the sample to said first level at which the whereby measurements of said variable are made sample is again stable as a single phase, each said concurrently with the application of, the thermal second level being different from the immediately pulses, and at least one said measurement is made preceding second level, at least one such change while the sample is in a metastable state. from one level to another causing the sample to 11. Apparatus as claimed in claim 10, comprising means for irradiating the sample with electro-magnetic radiation; means for measuring the intensity of radiation scattered in the sample; and means for measuring the sample temperature.

exchange relationship with the sample containing means, and Y c. heating means selectively operable to heat the 12. Apparatus as claimed in claim 11, wherein said sample containing means comprises'a capillary cell.

@293? UNITED STATES PATENT brute 31 2 CERTIFICATE 0F CORRECTIDN Patent No. 3,807,865 Dated April 30, 1974 Inventor(s) Manfred Gordon et a1 It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

t" f l "1 Column 1, line 45: "phenomenen" should read I phenonmenon Column 2, line 36: "change" should read changes Colum 2, lines 61-63: 3 3 v 2 I I acrltlcal State (2- 3H 2 m IHW Q (1 (6 2.

where-x gQKl-Qi) should read I v a 3 2 2' w -2 Critical State 9 w; 6 )T m lm a 1 e-as 2.

where g(l) Column 3 line 7; "polystrene" should read polystyrene Column 3, line 36: "reheated to to" should read reheated Column 4, line 52; "pumped by' should read pumped by a Column 9 line '6, claim 10: "cample" should read sample Column 10, line 10, claim 10: "s pinodal of critical point,"- should read spinodal or critical point,

Signed and sealed this 22nd day of October 1974.

(SEAL) Atteet:

I MCCOY M. GIBSON JR. c. MARSHALL DANN FR Attesting Officer Commissioner of Patents 

1. A process for determining spinodal loci associated with phase transition in samples of chemical solutions, which process comprises
 1. applying to said sample a series of thermal pulses, each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample substantially to said first level at which the sample is again stable as a single phase, each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability,
 2. measuring the temperature at each said second level for each such applied thermal pulse,
 3. measuring, concurrently with the application of the thermal pulses, a physical variable of the sample which changes strongly with temperature around the spinodal point and,
 4. determining the spinodal temperature from the measured values of the physical variable and the corresponding measured temperatures.
 2. measuring the temperature at each said second level for each applied thermal pulse
 2. A process as claimed in claim 1, in which the physical variable measured is a change in the distribution of sizes of particles or inhomogeneities.
 2. measuring the temperature at each said second level for each such applied thermal pulse,
 2. means for applying to a sample contained in said cample containing means a series of thermal pulses each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample to said first level at which the sample is again stable as a single phase, each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability, said means including a. a temperature controlled fluid bath, b. means for passing fluid from the bath into heat exchange relationship with the sample containing means, and c. heating means selectively operable to heat the fluid adjacent the sample whereby supplying the fluid from the bath without operation of said heating means produces the lower temperature of each thermal pulse and heating the fluid adjacent the sample produces the higher temperature level of each pulse, and
 2. means for applying to a sample contained in said sample containing means a series of thermal pulses each of which changes the temperature of the sample relatively rapidly from a first level at which the sample is in a stable state as a single phase to a second level, and subsequently returns the temperature of the sample to said first level at which the sample is again stable as a single phase, each said second level being different from the immediately preceding second level, at least one such change from one level to another causing the sample to pass through a phase transition temperature into a region of metastability, said means including a. a first temperature controlled fluid bath, b. a second fluid bath having a controlled temperature which is different from that of said first bath, c. means for slowly changing the temperature of one of said fluid baths, and d. means for passing fluid from the baths alternately into heat exchange relationship with the sample containing means to thereby apply said thermal pulses to the sample, said second fluid bath being maintained at a substantially constant temperature at least during each measurement conducted in the hereinafter described measuring means, and
 3. measuring means communicating with the sample containing means for measuring a physical variable of the sample, which variable changes strongly with temperature around the spinodal or critical point, whereby measurements of said variable are made concurrently with the application of the thermal pulses, and at least one said measurement is made while the sample is in a metastable state.
 3. measuring means communicating with the sample containing means for measuring a physical variable of the sample which variable changes strongly with temperature around the spinodal of critical point, whereby measurements of said variable are made concurrently with the application of the thermal pulses, and at least one said measurement is made while the sample is in a metastable state.
 3. measuring concurrently with the application of the thermal pulses, the intensity of radiation scattered by the sample or the turbidity of the sample, one or more such measurements being effected while the sample is in a metastable state, and
 3. measuring, concurrently with the application of the thermal pulses, a physical variable of the sample which changes strongly with temperature around the spinodal point and,
 3. A process as claimed in claim 1, in which the physical variable measured is the intensity of scattered electromagnetic radiation.
 4. determining the spinodal temperature from the measured values of the physical variable and the corresponding measured temperatures.
 4. A process for determining critical loci, said process comprising carrying out the process as claimed in claim 1 and performing cloud point measurements on the sample, the critical loci being determined by using the known thermodynamic condition of tangency relating to critical and spinodal loci.
 4. locating the spinodal temperature by extrapolation of reciprocal turbidity or reciprocal scattering intensity measurements obtained at the measured temperature levels of the series of pulses.
 5. A process for determining spinodal loci associated with phase transition in samples of chemical solutions, which process comprises
 6. A process for determining critical loci, said process comprising carrying out the process as claimed in claim 5 and performing cloud point measurements on the sample, the critical loci being determined by using the known thermodynamic condition of tangency relating to critical and spinodal loci.
 7. Apparatus for determining spinodal loci associated with phase transition in samples of chemical solutions, comprising
 8. Apparatus as claimed in claim 7, comprising means for irradiating the sample with electro-magnetic radiation; means for measuring the intensity of radiation scattered by the sample; and means for measuring the sample temperature.
 9. Apparatus as claimed in claim 8 in which said sample containing means comprises a capillary cell.
 10. Apparatus for determining spinodal loci associated with phase transition in samples of chemical solutions, comprising
 11. Apparatus as claimed in claim 10, comprising means for irradiating the sample with electro-magnetic radiation; means for measuring the intensity of radiation scattered in the sample; and means for measuring the sample temperature.
 12. Apparatus as claimed in claim 11, wherein said sample containing means comprises a capillary cell. > 